The answer is both OR a matter of opinion. See below:
* Australia is separated from all other continents by young oceanic crust. Greenland is geologically part of North America.
* Australia has highly distinct plants and animals. Greenland's are largely shared with northern North America.
* Australia is considerably larger than Greenland. If separation is key, then Antarctica should also be considered an island (making Australia second largest).
* Australia has unique, ancient cultures. Greenland's Arctic cultures, while unique, are part of larger North American Arctic culture.
* Everyone agrees that everything smaller than Australia is an island. Australians themselves are divided, and often claim that Australia is both the world's largest island and the world's smallest continent.
So, there are good reasons to assert that Australia is a continent and not an island.
However, it has to be conceded that there can be no definitive answer. The questions only grow more complex when you look at the details:
* By scientific criteria, Madagascar and several other islands are continents.
* Europe is really just a series of peninsulas off western Asia. Only culture, tradition, and a sense of separateness gave it continental status.
* Siberia and Alaska are not part of separate continents geologically. The sea barrier between them is just a happenstance of the current high sea levels of this interglacial period.
* Africa is solidly joined to southwest Asia, though in the process of rifting away.
* The Americas are joined by a substantial but recent land bridge.